The individual NN is defined by the same network topology for given
atomic species. It specifies the number of neurons formally named
here \(y^{N,l}_{i,j}\)  and their connectivity through the weights,
\(w^{N,l}_{i,j}\) , and called a Multi-Layer Perceptron (MLP). The
weights associated with each node pair are optimized during the
learning process by a Feed-Forward technique [1]}.
Thus, each of the \(M\)  layers within the neural network consists of
sets of nodes receiving multiple inputs from the previous layer and
passing outputs to the next layer. Here a fully connected network
is used, in which every output of a layer is an input for every
neuron in the next layer. The corresponding mathematical description
is as follows: the input signals are linearly
combined before being activated by function \(f\)  to give each output
\(y^{N,l}_i\)  of a given fully connected layer \(l\)  as
\(y_i^{N,l} = f \left(\sum _{j=1}^{M_{l-1}}w_{i,j}^{N,l}y_j^{N,l-1}+b_i^{N,l}\right),\) 
